Elastic constants of highly aligned fibre composites

2 Elastic constants of highly aligned fibre composites 

We take up the discussion following Section 8.2.1 above. In a conventional fibre composite a matrix of moderate stiffness ( 1 GPa) is reinforced with a stiff and strong fibre (of modulus 100 GPa). Most usually this is glass or carbon fibre, but high-strength fibres such as aramid or polyethylene fibres are also used. 

It is instructive to consider the calculation of the elastic constants for an undirectional fibre composite consisting of perfectly aligned fibres of infinite length. It is assumed that there is excellent adhesion between the fibres and the matrix. 

The simplest approach is to extend the assumptions of Equations (8.3) and (8.5). Choosing the fibre direction as the 3 axis, the assumptions of homogeneous strain in the 3 direction and homogeneous stress in the 1 direction imply, in terms of the nomenclature proposed in Section 7.1.1, that the five independent elastic constants for the composite E, E, vfj, v 2 and Gl) are given by 

Consider a perfectly aligned fibre composite reinforced with isotropic fibres of 

2 Elastic Constants of Highly Aligned Fibre Composites 

Consider a perfectly aligned fibre composite reinforced with isotropic fibres of infinite stiffness in an isotropic matrix of modulus E and Poisson s ratio v . In the matrix we have 

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